Given the sequence 192, -144, 108...
[tex]\begin{gathered} \text{ r=}\frac{-144}{192}=-0.75 \\ r=\frac{108}{-144}=-0.75 \end{gathered}[/tex]The sequence has a common ratio. It is a geometric sequence.
the nth term of a Geometric sequence is given by the formula
[tex]\begin{gathered} T_n=ar^{n-1} \\ \text{Where a = 192, r=-0.75=-3/4} \\ T_n=192(\frac{-3}{4})^{n-1} \\ T_n=192\text{ x }(\frac{-3}{4})^n.\text{ }(\frac{-3}{4})^{-1} \\ =192\text{ x }(\frac{-3}{4})^{n\text{ }}\text{ (}\frac{-4}{3}) \\ =192(\frac{-4}{3})(\frac{-3}{4})^n \\ =-256(\frac{-3}{4})^n \\ \\ \text{Hence, The nth term is }-256(\frac{-3}{4})^n \end{gathered}[/tex]
